Calculus Writing Assignment: Related Rates Each problem is worth 5 points. Total Points: 50 Answer each of the problems. Make sure to show all your work. 1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, at what rate is the volume increasing when the radius is 5 inches? 2. A particle moves in a circular orbit x2 + y2 = 16. As it passes through the point (2, 2 3 ), its y-coordinate decreases at a rate of 3 units per second. At what rate is the xcoordinate changing? 3. A point moves along the straight line x + 3y = 6. Find the rate of change of the y-coordinate, given that the x-coordinate is increasing at a rate of 3 units per second. 4. If a point is moving along y = 3x2 - 4x - 6 at a rate of dx = 4 m/s, find dt dy , when x = 3. dt 5. A heap of garbage in the shape of a cube is being compacted. Given that the volume decreases at a rate of 2 cubic meters per minute, find the rate of change of an edge of the cube when the volume is exactly 27 cubic meters. 6. A circle with area A = r 2 is expanding with time. If 7. A triangle, whose h = 2b, has an area A = 8 cm2/s, what is dA dr = 5 cm2/s, what is when r = 6? dt dt 1 1 dA bh = b(2b) = b2 is expanding with time. If = dt 2 2 db when b = 2? dt 8. A sphere is expanding at the rate of 8 cm3/sec, the formula for volume of a sphere is V = what is 4 3 r , 3 dr when r = 5? dt 9. A cone is expanding at the rate of 9 cm3/sec, the formula for volume of a cone is: V = h = 2r, what is r 2h , let 3 dr when r = 3? dt 10. A cylinder is being filled such that the height of its contents is increasing at a rate of 5 cm /s. What is the rate of change of the volume if r = 3 and V = r2h